This paper is going to address the issue of combining loudspeakers
to increase the area of coverage from that of an individual
loudspeaker. The concept is generally referred to as arraying
the enclosures. Proper arraying insures even coverage with
a minimum of mutual interference, and thus allows the sound
system to perform as near to a single source as possible.

When dealing with multiples of loudspeaker enclosures, the
main concern is to maintain the integrity of the high frequency
devices. The modern highest quality sound reinforcement loudspeaker
enclosures exhibit a high frequency horn that offers uniform
frequency response with dispersion; they are said to be constant
in their directivity or CD for short. There are still a lot
of older horns out there that do not have constant directivity,
or a well controlled pattern of coverage. These older horns
are referred to as exponential radial horns. By exponential
we mean that the rate of flare or taper of the horn increases
with the square of the distance away from the throat or entry
of the horn. Exponential radial horns do not direct the high
frequency information very smoothly, with these horns the high
frequency coverage is that of a very narrow beam (usually less
than 20 degrees) directly on-axis to the horn. The taper or
flares rates of the exponential radial horn are too rapid to
allow the air molecules carrying the high frequency information
to the cling to the side walls of the horn so they can be directed
over a wider area of coverage. The reason constant directivity
horns do a much better job is that their rates of flare or
taper vary as the sound enters the throat area and moves throughout
the horn's boundaries, they are said to be multi-taper and
multi-flare. It is this variation of conditions within the
sidewalls of the horn that allows for the much-improved high
fidelity of the loudspeaker system. This paper assumes that
the reader is going to utilize constant directivity high frequency
devices in the design of the loudspeaker array.

It needs to be mentioned at this time, that all constant directivity
horns require a special type of equalization, commonly called
CD EQ, to maintain a flat frequency response. When we succeeded
in directing the high frequency information into a wider pattern,
we subsequently reduced the level of the highs as well. All
constant directivity horns have a high frequency roll off rate
of -6 dB or more. A compensatory equalization is employed to
maintain a flat frequency response. This equalization is part
of the systems crossover design. So this paper assumes that
the reader will employ loudspeaker systems with constant directivity
horns, with the appropriate equalization as the building blocks
of the arrays we are going to discuss.

The biggest mistake or improper application involving systems
with constant directivity horns is that when some individuals
use them in multiples, they don't take into account the individual
coverage patterns and therefore allow the high frequency devices
(horns) to overlap in their areas of coverage. Some small or
very modest amount of overlap is sometimes necessary and acceptable.
However, severe overlapping of coverage (more than 10 degrees)
results in interference patterns commonly called lobbing or
fingering of the pattern. Remember sound is propagated through
the medium of air by the vibrations of the individual air molecules
bumping into one another in a pattern that exhibits a wave
through the atmosphere. When air molecules bump into one another
there is a reaction. For every action is there is an equal
and opposite reaction (Sir Isaac Newton). If two billiard balls
are traveling at an angle toward the center of a pool table,
and are allowed to collide, will they not bounce off of each
other at the same angle of their collision? What would make
you think that solid air molecules would react any differently?
The angle of incidence is equal to the angle of coincidence,
or the angle of arrival is equal to the angle of departure.

It is the high frequency information that contains those components
of speech that allows us to distinguish the consonant and sibilant
sounds that make speech intelligible. Those portions of speech
created with the lips and tongue are most important if the
system is to have clarity, transparency, and general intelligibility.
The word sibilance almost defines itself by the mere pronunciation
of the word. It is the sibilant components of speech that allow
us to distinguish words from another, words like float, tote,
boat, and moat, or dog, log, and frog as examples. If the high
frequency information is to be most transparent, i.e., intelligible,
multiple loudspeakers must be placed with forethought as to
the manner in which the horns will combine to retain the concept
of constant directivity of the high frequencies emanating from
the array of individual loudspeaker components.

Some definitions first. The Direct Field is that sound field
emanating directly from a source and not significantly influenced
by any of the boundaries within the room or acoustic space.
Since all rooms have boundaries in the form of the ceiling,
floor, and walls, eventually some sound will arrive at those
surfaces. When sound strikes a solid surface, some small amount
sound energy is absorbed due to the friction or heat created
in the encounter with the boundary, but the majority of the
energy is reflected off of the boundary. This reflected energy
is called reverberation or the reverberant sound field, meaning
that it is independent and no longer part of the direct field.
The first concept I want to express then is that; any direct
field that does not arrive at the ear of the listener is wasted
energy. In other words, it is best to minimize that sound energy
that arrives at the room's surface boundaries. Acoustic energy
that does not reach the listener is wasted energy. So the first
concept is, "Point the loudspeaker at the audience or congregation,
and they will hear it better" (what a concept!). I am continuously
amazed by the number of systems installed in churches and auditoriums
where the directional components (high frequency horns) are
not even directed to the listener's ear at all.

The next definition is for Critical Distance. Critical Distance
is that point within a room or acoustic space where the level
of the reverberant energy field and the level of the direct
sound field are equal. Once you step beyond the point of critical
distance, the reverberant level is greater than the direct
sound level. The farther you move beyond the critical distance
point, the reverberant field tends to mask or cover the direct
field. A fairly simple and straightforward test can be conducted
in any church to ascertain the approximate point of critical
distance in any church sanctuary. You see the church has a
critical distance point within its acoustical space, with and
without the sound system turned on. It is a good idea to establish
the point of critical distance without the sound system first,
then conduct the same test employing the sound reinforcement
system. The properly installed sound system should move the
natural (unassisted) point of critical distance dramatically
further out into the listening area. However don't be too surprised
if after conducting both the assisted and unassisted tests,
if the assisted or reinforced test exhibits an even shorter
critical distance measurement. If this is the case, the sound
system is of an inappropriate design for that room.

Finding the critical distance point in the church sanctuary
can be done with one person acting as the speaking source and
two to four subjects acting as the listeners. With the sound
system off, have the speaker read a passage from the Bible
while standing at the pulpit. (Note: It is
best to use a speaker with a normal voice, like the actor,
Richard Harris, who has a trained voice projected from the
diaphragm and would be more easily understood at a distance
than a normal talker.) Have the listeners stand a couple of
feet in front of the pulpit, have them listen to the person
speaking without looking directly at them (keep their eyes
directed), and have them slowly back up the center aisle of
the church. Instruct the listeners to raise their hands when
they perceive that sound is no longer coming directly from
the direction of the person speaking. As you slowly back away
there will be a point at which the sound is still understood
but it no longer appears to come directly from the source,
it just appears to be there. If the listeners are of normal
binaural hearing, i.e., both ears work equally well, they should
come to within 12 to 18 inches of agreement as to the point
in the room where the sound no longer appears to come from
the pulpit. After this point is determined, turn on the sound
system and repeat the test while speaking into the pulpit microphone.
If the system is designed well, there should be a much greater
distance from the pulpit to the critical distance point with
speech reinforcement. Experiment with this test as it can show
you a lot about the acoustics of your church sanctuary and
the degree to which your existing sound system is effective.